<h2>题目编号 : 104</h2>
<div style="color:#666;font-size:80%;">09 September 2005</div><br />
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<p>The Fibonacci sequence is defined by the recurrence relation:</p>
<blockquote>F<img src="" style="display:none;" alt="_(" /><sub><i>n</i></sub><img src="" style="display:none;" alt=")" /> = F<img src="" style="display:none;" alt="_(" /><sub><i>n</i><img src='images/symbol_minus.gif' width='9' height='3' alt='&minus;' border='0' style='vertical-align:middle;' />1</sub><img src="" style="display:none;" alt=")" /> + F<img src="" style="display:none;" alt="_(" /><sub><i>n</i><img src='images/symbol_minus.gif' width='9' height='3' alt='&minus;' border='0' style='vertical-align:middle;' />2</sub><img src="" style="display:none;" alt=")" />, where F<img src="" style="display:none;" alt="_(" /><sub>1</sub><img src="" style="display:none;" alt=")" /> = 1 and F<img src="" style="display:none;" alt="_(" /><sub>2</sub><img src="" style="display:none;" alt=")" /> = 1.</blockquote>
<p>It turns out that F<img src="" style="display:none;" alt="_(" /><sub>541</sub><img src="" style="display:none;" alt=")" />, which contains 113 digits, is the first Fibonacci number for which the last nine digits are 1-9 pandigital (contain all the digits 1 to 9, but not necessarily in order). And F<img src="" style="display:none;" alt="_(" /><sub>2749</sub><img src="" style="display:none;" alt=")" />, which contains 575 digits, is the first Fibonacci number for which the first nine digits are 1-9 pandigital.</p>
<p>Given that F<img src="" style="display:none;" alt="_(" /><sub><i>k</i></sub><img src="" style="display:none;" alt=")" /> is the first Fibonacci number for which the first nine digits AND the last nine digits are 1-9 pandigital, find <i>k</i>.</p>

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